From: Sage Weil Date: Wed, 3 Dec 2014 01:26:51 +0000 (-0800) Subject: crush: add a straw2 bucket type X-Git-Tag: v0.93~161^2~6 X-Git-Url: http://git-server-git.apps.pok.os.sepia.ceph.com/?a=commitdiff_plain;h=242293c908e923d474910f2b8203fa3b41eb5a53;p=ceph.git crush: add a straw2 bucket type This is an improved straw bucket that correctly avoids any data movement between items A and B when neither A nor B's weights are changed. Said differently, if we adjust the weight of item C (including adding it anew or removing it completely), we will only see inputs move to or from C, never between other items in the bucket. Notably, there is not intermediate scaling factor that needs to be calculated. The mapping function is a simple function of the item weights. Unfortunately, we need a natural log, which is expensive. We use a lookup table here. Signed-off-by: Sage Weil --- diff --git a/src/crush/CrushCompiler.cc b/src/crush/CrushCompiler.cc index 33ed1dbfac07..0e266cd3f886 100644 --- a/src/crush/CrushCompiler.cc +++ b/src/crush/CrushCompiler.cc @@ -439,6 +439,8 @@ int CrushCompiler::parse_bucket(iter_t const& i) alg = CRUSH_BUCKET_TREE; else if (a == "straw") alg = CRUSH_BUCKET_STRAW; + else if (a == "straw2") + alg = CRUSH_BUCKET_STRAW2; else { err << "unknown bucket alg '" << a << "'" << std::endl << std::endl; return -EINVAL; diff --git a/src/crush/CrushWrapper.cc b/src/crush/CrushWrapper.cc index 1d00b994bb05..0c7502bd1688 100644 --- a/src/crush/CrushWrapper.cc +++ b/src/crush/CrushWrapper.cc @@ -1081,6 +1081,12 @@ void CrushWrapper::encode(bufferlist& bl, bool lean) const } break; + case CRUSH_BUCKET_STRAW2: + for (unsigned j=0; jbuckets[i]->size; j++) { + ::encode((reinterpret_cast(crush->buckets[i]))->item_weights[j], bl); + } + break; + default: assert(0); break; @@ -1229,6 +1235,9 @@ void CrushWrapper::decode_crush_bucket(crush_bucket** bptr, bufferlist::iterator case CRUSH_BUCKET_STRAW: size = sizeof(crush_bucket_straw); break; + case CRUSH_BUCKET_STRAW2: + size = sizeof(crush_bucket_straw2); + break; default: { char str[128]; @@ -1292,6 +1301,15 @@ void CrushWrapper::decode_crush_bucket(crush_bucket** bptr, bufferlist::iterator break; } + case CRUSH_BUCKET_STRAW2: { + crush_bucket_straw2* cbs = reinterpret_cast(bucket); + cbs->item_weights = (__u32*)calloc(1, bucket->size * sizeof(__u32)); + for (unsigned j = 0; j < bucket->size; ++j) { + ::decode(cbs->item_weights[j], blp); + } + break; + } + default: // We should have handled this case in the first switch statement assert(0); diff --git a/src/crush/builder.c b/src/crush/builder.c index faa586e699b1..7e611906bd84 100644 --- a/src/crush/builder.c +++ b/src/crush/builder.c @@ -603,6 +603,52 @@ err: return NULL; } +struct crush_bucket_straw2 * +crush_make_straw2_bucket(struct crush_map *map, + int hash, + int type, + int size, + int *items, + int *weights) +{ + struct crush_bucket_straw2 *bucket; + int i; + + bucket = malloc(sizeof(*bucket)); + if (!bucket) + return NULL; + memset(bucket, 0, sizeof(*bucket)); + bucket->h.alg = CRUSH_BUCKET_STRAW2; + bucket->h.hash = hash; + bucket->h.type = type; + bucket->h.size = size; + + bucket->h.items = malloc(sizeof(__s32)*size); + if (!bucket->h.items) + goto err; + bucket->h.perm = malloc(sizeof(__u32)*size); + if (!bucket->h.perm) + goto err; + bucket->item_weights = malloc(sizeof(__u32)*size); + if (!bucket->item_weights) + goto err; + + bucket->h.weight = 0; + for (i=0; ih.items[i] = items[i]; + bucket->h.weight += weights[i]; + bucket->item_weights[i] = weights[i]; + } + + return bucket; +err: + free(bucket->item_weights); + free(bucket->h.perm); + free(bucket->h.items); + free(bucket); + return NULL; +} + struct crush_bucket* @@ -629,6 +675,8 @@ crush_make_bucket(struct crush_map *map, case CRUSH_BUCKET_STRAW: return (struct crush_bucket *)crush_make_straw_bucket(map, hash, type, size, items, weights); + case CRUSH_BUCKET_STRAW2: + return (struct crush_bucket *)crush_make_straw2_bucket(map, hash, type, size, items, weights); } return 0; } @@ -808,6 +856,42 @@ int crush_add_straw_bucket_item(struct crush_map *map, return crush_calc_straw(map, bucket); } +int crush_add_straw2_bucket_item(struct crush_map *map, + struct crush_bucket_straw2 *bucket, + int item, int weight) +{ + int newsize = bucket->h.size + 1; + + void *_realloc = NULL; + + if ((_realloc = realloc(bucket->h.items, sizeof(__s32)*newsize)) == NULL) { + return -ENOMEM; + } else { + bucket->h.items = _realloc; + } + if ((_realloc = realloc(bucket->h.perm, sizeof(__u32)*newsize)) == NULL) { + return -ENOMEM; + } else { + bucket->h.perm = _realloc; + } + if ((_realloc = realloc(bucket->item_weights, sizeof(__u32)*newsize)) == NULL) { + return -ENOMEM; + } else { + bucket->item_weights = _realloc; + } + + bucket->h.items[newsize-1] = item; + bucket->item_weights[newsize-1] = weight; + + if (crush_addition_is_unsafe(bucket->h.weight, weight)) + return -ERANGE; + + bucket->h.weight += weight; + bucket->h.size++; + + return 0; +} + int crush_bucket_add_item(struct crush_map *map, struct crush_bucket *b, int item, int weight) { @@ -823,6 +907,8 @@ int crush_bucket_add_item(struct crush_map *map, return crush_add_tree_bucket_item((struct crush_bucket_tree *)b, item, weight); case CRUSH_BUCKET_STRAW: return crush_add_straw_bucket_item(map, (struct crush_bucket_straw *)b, item, weight); + case CRUSH_BUCKET_STRAW2: + return crush_add_straw2_bucket_item(map, (struct crush_bucket_straw2 *)b, item, weight); default: return -1; } @@ -1034,6 +1120,50 @@ int crush_remove_straw_bucket_item(struct crush_map *map, return crush_calc_straw(map, bucket); } +int crush_remove_straw2_bucket_item(struct crush_map *map, + struct crush_bucket_straw2 *bucket, int item) +{ + int newsize = bucket->h.size - 1; + unsigned i, j; + + for (i = 0; i < bucket->h.size; i++) { + if (bucket->h.items[i] == item) { + bucket->h.size--; + if (bucket->item_weights[i] < bucket->h.weight) + bucket->h.weight -= bucket->item_weights[i]; + else + bucket->h.weight = 0; + for (j = i; j < bucket->h.size; j++) { + bucket->h.items[j] = bucket->h.items[j+1]; + bucket->item_weights[j] = bucket->item_weights[j+1]; + } + break; + } + } + if (i == bucket->h.size) + return -ENOENT; + + void *_realloc = NULL; + + if ((_realloc = realloc(bucket->h.items, sizeof(__s32)*newsize)) == NULL) { + return -ENOMEM; + } else { + bucket->h.items = _realloc; + } + if ((_realloc = realloc(bucket->h.perm, sizeof(__u32)*newsize)) == NULL) { + return -ENOMEM; + } else { + bucket->h.perm = _realloc; + } + if ((_realloc = realloc(bucket->item_weights, sizeof(__u32)*newsize)) == NULL) { + return -ENOMEM; + } else { + bucket->item_weights = _realloc; + } + + return 0; +} + int crush_bucket_remove_item(struct crush_map *map, struct crush_bucket *b, int item) { /* invalidate perm cache */ @@ -1048,6 +1178,8 @@ int crush_bucket_remove_item(struct crush_map *map, struct crush_bucket *b, int return crush_remove_tree_bucket_item((struct crush_bucket_tree *)b, item); case CRUSH_BUCKET_STRAW: return crush_remove_straw_bucket_item(map, (struct crush_bucket_straw *)b, item); + case CRUSH_BUCKET_STRAW2: + return crush_remove_straw2_bucket_item(map, (struct crush_bucket_straw2 *)b, item); default: return -1; } @@ -1140,6 +1272,26 @@ int crush_adjust_straw_bucket_item_weight(struct crush_map *map, return diff; } +int crush_adjust_straw2_bucket_item_weight(struct crush_map *map, + struct crush_bucket_straw2 *bucket, + int item, int weight) +{ + unsigned idx; + int diff; + + for (idx = 0; idx < bucket->h.size; idx++) + if (bucket->h.items[idx] == item) + break; + if (idx == bucket->h.size) + return 0; + + diff = weight - bucket->item_weights[idx]; + bucket->item_weights[idx] = weight; + bucket->h.weight += diff; + + return diff; +} + int crush_bucket_adjust_item_weight(struct crush_map *map, struct crush_bucket *b, int item, int weight) @@ -1158,6 +1310,10 @@ int crush_bucket_adjust_item_weight(struct crush_map *map, return crush_adjust_straw_bucket_item_weight(map, (struct crush_bucket_straw *)b, item, weight); + case CRUSH_BUCKET_STRAW2: + return crush_adjust_straw2_bucket_item_weight(map, + (struct crush_bucket_straw2 *)b, + item, weight); default: return -1; } @@ -1263,6 +1419,28 @@ static int crush_reweight_straw_bucket(struct crush_map *crush, struct crush_buc return 0; } +static int crush_reweight_straw2_bucket(struct crush_map *crush, struct crush_bucket_straw2 *bucket) +{ + unsigned i; + + bucket->h.weight = 0; + for (i = 0; i < bucket->h.size; i++) { + int id = bucket->h.items[i]; + if (id < 0) { + struct crush_bucket *c = crush->buckets[-1-id]; + crush_reweight_bucket(crush, c); + bucket->item_weights[i] = c->weight; + } + + if (crush_addition_is_unsafe(bucket->h.weight, bucket->item_weights[i])) + return -ERANGE; + + bucket->h.weight += bucket->item_weights[i]; + } + + return 0; +} + int crush_reweight_bucket(struct crush_map *crush, struct crush_bucket *b) { switch (b->alg) { @@ -1274,6 +1452,8 @@ int crush_reweight_bucket(struct crush_map *crush, struct crush_bucket *b) return crush_reweight_tree_bucket(crush, (struct crush_bucket_tree *)b); case CRUSH_BUCKET_STRAW: return crush_reweight_straw_bucket(crush, (struct crush_bucket_straw *)b); + case CRUSH_BUCKET_STRAW2: + return crush_reweight_straw2_bucket(crush, (struct crush_bucket_straw2 *)b); default: return -1; } diff --git a/src/crush/crush.c b/src/crush/crush.c index bf856fc832a8..c45b6f501b22 100644 --- a/src/crush/crush.c +++ b/src/crush/crush.c @@ -18,6 +18,7 @@ const char *crush_bucket_alg_name(int alg) case CRUSH_BUCKET_LIST: return "list"; case CRUSH_BUCKET_TREE: return "tree"; case CRUSH_BUCKET_STRAW: return "straw"; + case CRUSH_BUCKET_STRAW2: return "straw2"; default: return "unknown"; } } diff --git a/src/crush/crush.h b/src/crush/crush.h index 8ce146976500..b2628bf24f46 100644 --- a/src/crush/crush.h +++ b/src/crush/crush.h @@ -100,13 +100,15 @@ struct crush_rule { * uniform O(1) poor poor * list O(n) optimal poor * tree O(log n) good good - * straw O(n) optimal optimal + * straw O(n) better better + * straw2 O(n) optimal optimal */ enum { CRUSH_BUCKET_UNIFORM = 1, CRUSH_BUCKET_LIST = 2, CRUSH_BUCKET_TREE = 3, - CRUSH_BUCKET_STRAW = 4 + CRUSH_BUCKET_STRAW = 4, + CRUSH_BUCKET_STRAW2 = 5, }; extern const char *crush_bucket_alg_name(int alg); @@ -153,6 +155,11 @@ struct crush_bucket_straw { __u32 *straws; /* 16-bit fixed point */ }; +struct crush_bucket_straw2 { + struct crush_bucket h; + __u32 *item_weights; /* 16-bit fixed point */ +}; + /* @@ -203,6 +210,7 @@ extern void crush_destroy_bucket_uniform(struct crush_bucket_uniform *b); extern void crush_destroy_bucket_list(struct crush_bucket_list *b); extern void crush_destroy_bucket_tree(struct crush_bucket_tree *b); extern void crush_destroy_bucket_straw(struct crush_bucket_straw *b); +extern void crush_destroy_bucket_straw2(struct crush_bucket_straw2 *b); extern void crush_destroy_bucket(struct crush_bucket *b); extern void crush_destroy_rule(struct crush_rule *r); extern void crush_destroy(struct crush_map *map); diff --git a/src/crush/crush_ln_table.h b/src/crush/crush_ln_table.h new file mode 100644 index 000000000000..92741ed99b88 --- /dev/null +++ b/src/crush/crush_ln_table.h @@ -0,0 +1,6556 @@ +static uint16_t crush_ln_table[65536] = { + 0x0,0x1000,0x195c,0x2000,0x2526,0x295c,0x2cea,0x3000,0x32b8,0x3526, + 0x3759,0x395c,0x3b35,0x3cea,0x3e82,0x4000,0x4166,0x42b8,0x43f7,0x4526, + 0x4646,0x4759,0x4860,0x495c,0x4a4d,0x4b35,0x4c14,0x4cea,0x4dba,0x4e82, + 0x4f44,0x5000,0x50b5,0x5166,0x5211,0x52b8,0x5359,0x53f7,0x5491,0x5526, + 0x55b8,0x5646,0x56d1,0x5759,0x57de,0x5860,0x58df,0x595c,0x59d5,0x5a4d, + 0x5ac2,0x5b35,0x5ba5,0x5c14,0x5c80,0x5cea,0x5d53,0x5dba,0x5e1f,0x5e82, + 0x5ee4,0x5f44,0x5fa2,0x6000,0x605b,0x60b5,0x610e,0x6166,0x61bc,0x6211, + 0x6265,0x62b8,0x6309,0x6359,0x63a9,0x63f7,0x6444,0x6491,0x64dc,0x6526, + 0x6570,0x65b8,0x6600,0x6646,0x668c,0x66d1,0x6716,0x6759,0x679c,0x67de, + 0x681f,0x6860,0x68a0,0x68df,0x691e,0x695c,0x6999,0x69d5,0x6a11,0x6a4d, + 0x6a88,0x6ac2,0x6afb,0x6b35,0x6b6d,0x6ba5,0x6bdd,0x6c14,0x6c4a,0x6c80, + 0x6cb5,0x6cea,0x6d1f,0x6d53,0x6d87,0x6dba,0x6ded,0x6e1f,0x6e51,0x6e82, + 0x6eb3,0x6ee4,0x6f14,0x6f44,0x6f73,0x6fa2,0x6fd1,0x7000,0x702d,0x705b, + 0x7088,0x70b5,0x70e2,0x710e,0x713a,0x7166,0x7191,0x71bc,0x71e7,0x7211, + 0x723b,0x7265,0x728e,0x72b8,0x72e0,0x7309,0x7331,0x7359,0x7381,0x73a9, + 0x73d0,0x73f7,0x741e,0x7444,0x746b,0x7491,0x74b6,0x74dc,0x7501,0x7526, + 0x754b,0x7570,0x7594,0x75b8,0x75dc,0x7600,0x7623,0x7646,0x766a,0x768c, + 0x76af,0x76d1,0x76f4,0x7716,0x7738,0x7759,0x777b,0x779c,0x77bd,0x77de, + 0x77ff,0x781f,0x7840,0x7860,0x7880,0x78a0,0x78c0,0x78df,0x78fe,0x791e, + 0x793d,0x795c,0x797a,0x7999,0x79b7,0x79d5,0x79f3,0x7a11,0x7a2f,0x7a4d, + 0x7a6a,0x7a88,0x7aa5,0x7ac2,0x7adf,0x7afb,0x7b18,0x7b35,0x7b51,0x7b6d, + 0x7b89,0x7ba5,0x7bc1,0x7bdd,0x7bf8,0x7c14,0x7c2f,0x7c4a,0x7c65,0x7c80, + 0x7c9b,0x7cb5,0x7cd0,0x7cea,0x7d05,0x7d1f,0x7d39,0x7d53,0x7d6d,0x7d87, + 0x7da0,0x7dba,0x7dd3,0x7ded,0x7e06,0x7e1f,0x7e38,0x7e51,0x7e69,0x7e82, + 0x7e9b,0x7eb3,0x7ecc,0x7ee4,0x7efc,0x7f14,0x7f2c,0x7f44,0x7f5c,0x7f73, + 0x7f8b,0x7fa2,0x7fba,0x7fd1,0x7fe8,0x8000,0x8017,0x802d,0x8044,0x805b, + 0x8072,0x8088,0x809f,0x80b5,0x80cc,0x80e2,0x80f8,0x810e,0x8124,0x813a, + 0x8150,0x8166,0x817b,0x8191,0x81a7,0x81bc,0x81d1,0x81e7,0x81fc,0x8211, + 0x8226,0x823b,0x8250,0x8265,0x827a,0x828e,0x82a3,0x82b8,0x82cc,0x82e0, + 0x82f5,0x8309,0x831d,0x8331,0x8345,0x8359,0x836d,0x8381,0x8395,0x83a9, + 0x83bc,0x83d0,0x83e4,0x83f7,0x840a,0x841e,0x8431,0x8444,0x8457,0x846b, + 0x847e,0x8491,0x84a3,0x84b6,0x84c9,0x84dc,0x84ee,0x8501,0x8514,0x8526, + 0x8539,0x854b,0x855d,0x8570,0x8582,0x8594,0x85a6,0x85b8,0x85ca,0x85dc, + 0x85ee,0x8600,0x8611,0x8623,0x8635,0x8646,0x8658,0x866a,0x867b,0x868c, + 0x869e,0x86af,0x86c0,0x86d1,0x86e3,0x86f4,0x8705,0x8716,0x8727,0x8738, + 0x8749,0x8759,0x876a,0x877b,0x878b,0x879c,0x87ad,0x87bd,0x87ce,0x87de, + 0x87ef,0x87ff,0x880f,0x881f,0x8830,0x8840,0x8850,0x8860,0x8870,0x8880, + 0x8890,0x88a0,0x88b0,0x88c0,0x88cf,0x88df,0x88ef,0x88fe,0x890e,0x891e, + 0x892d,0x893d,0x894c,0x895c,0x896b,0x897a,0x8989,0x8999,0x89a8,0x89b7, + 0x89c6,0x89d5,0x89e4,0x89f3,0x8a02,0x8a11,0x8a20,0x8a2f,0x8a3e,0x8a4d, + 0x8a5b,0x8a6a,0x8a79,0x8a88,0x8a96,0x8aa5,0x8ab3,0x8ac2,0x8ad0,0x8adf, + 0x8aed,0x8afb,0x8b0a,0x8b18,0x8b26,0x8b35,0x8b43,0x8b51,0x8b5f,0x8b6d, + 0x8b7b,0x8b89,0x8b97,0x8ba5,0x8bb3,0x8bc1,0x8bcf,0x8bdd,0x8bea,0x8bf8, + 0x8c06,0x8c14,0x8c21,0x8c2f,0x8c3c,0x8c4a,0x8c58,0x8c65,0x8c73,0x8c80, + 0x8c8d,0x8c9b,0x8ca8,0x8cb5,0x8cc3,0x8cd0,0x8cdd,0x8cea,0x8cf8,0x8d05, + 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0xff08,0xff08,0xff08,0xff09,0xff09,0xff09,0xff09,0xff09,0xff09,0xff09, + 0xff09,0xff09,0xff09,0xff0a,0xff0a,0xff0a,0xff0a,0xff0a,0xff0a,0xff0a, + 0xff0a,0xff0a,0xff0a,0xff0a,0xff0b,0xff0b,0xff0b,0xff0b,0xff0b,0xff0b, + 0xff0b,0xff0b,0xff0b,0xff0b,0xff0b,0xff0c,0xff0c,0xff0c,0xff0c,0xff0c, + 0xff0c,0xff0c,0xff0c,0xff0c,0xff0c,0xff0d,0xff0d,0xff0d,0xff0d,0xff0d, + 0xff0d,0xff0d,0xff0d,0xff0d,0xff0d,0xff0d,0xff0e,0xff0e,0xff0e,0xff0e, + 0xff0e,0xff0e,0xff0e,0xff0e,0xff0e,0xff0e,0xff0f,0xff0f,0xff0f,0xff0f, + 0xff0f,0xff0f,0xff0f,0xff0f,0xff0f,0xff0f,0xff0f,0xff10,0xff10,0xff10, + 0xff10,0xff10,0xff10,0xff10,0xff10,0xff10,0xff10,0xff10,0xff11,0xff11, + 0xff11,0xff11,0xff11,0xff11,0xff11,0xff11,0xff11,0xff11,0xff12,0xff12, + 0xff12,0xff12,0xff12,0xff12,0xff12,0xff12,0xff12,0xff12,0xff12,0xff13, + 0xff13,0xff13,0xff13,0xff13,0xff13,0xff13,0xff13,0xff13,0xff13,0xff13, + 0xff14,0xff14,0xff14,0xff14,0xff14,0xff14,0xff14,0xff14,0xff14,0xff14, + 0xff15,0xff15,0xff15,0xff15,0xff15,0xff15,0xff15,0xff15,0xff15,0xff15, + 0xff15,0xff16,0xff16,0xff16,0xff16,0xff16,0xff16,0xff16,0xff16,0xff16, + 0xff16,0xff16,0xff17,0xff17,0xff17,0xff17,0xff17,0xff17,0xff17,0xff17, + 0xff17,0xff17,0xff18,0xff18,0xff18,0xff18,0xff18,0xff18,0xff18,0xff18, + 0xff18,0xff18,0xff18,0xff19,0xff19,0xff19,0xff19,0xff19,0xff19,0xff19, + 0xff19,0xff19,0xff19,0xff19,0xff1a,0xff1a,0xff1a,0xff1a,0xff1a,0xff1a, + 0xff1a,0xff1a,0xff1a,0xff1a,0xff1b,0xff1b,0xff1b,0xff1b,0xff1b,0xff1b, + 0xff1b,0xff1b,0xff1b,0xff1b,0xff1b,0xff1c,0xff1c,0xff1c,0xff1c,0xff1c, + 0xff1c,0xff1c,0xff1c,0xff1c,0xff1c,0xff1c,0xff1d,0xff1d,0xff1d,0xff1d, + 0xff1d,0xff1d,0xff1d,0xff1d,0xff1d,0xff1d,0xff1e,0xff1e,0xff1e,0xff1e, + 0xff1e,0xff1e,0xff1e,0xff1e,0xff1e,0xff1e,0xff1e,0xff1f,0xff1f,0xff1f, + 0xff1f,0xff1f,0xff1f,0xff1f,0xff1f,0xff1f,0xff1f,0xff1f,0xff20,0xff20, + 0xff20,0xff20,0xff20,0xff20,0xff20,0xff20,0xff20,0xff20,0xff21,0xff21, + 0xff21,0xff21,0xff21,0xff21,0xff21,0xff21,0xff21,0xff21,0xff21,0xff22, + 0xff22,0xff22,0xff22,0xff22,0xff22,0xff22,0xff22,0xff22,0xff22,0xff22, + 0xff23,0xff23,0xff23,0xff23,0xff23,0xff23,0xff23,0xff23,0xff23,0xff23, + 0xff24,0xff24,0xff24,0xff24,0xff24,0xff24,0xff24,0xff24,0xff24,0xff24, + 0xff24,0xff25,0xff25,0xff25,0xff25,0xff25,0xff25,0xff25,0xff25,0xff25, + 0xff25,0xff25,0xff26,0xff26,0xff26,0xff26,0xff26,0xff26,0xff26,0xff26, + 0xff26,0xff26,0xff26,0xff27,0xff27,0xff27,0xff27,0xff27,0xff27,0xff27, + 0xff27,0xff27,0xff27,0xff28,0xff28,0xff28,0xff28,0xff28,0xff28,0xff28, + 0xff28,0xff28,0xff28,0xff28,0xff29,0xff29,0xff29,0xff29,0xff29,0xff29, + 0xff29,0xff29,0xff29,0xff29,0xff29,0xff2a,0xff2a,0xff2a,0xff2a,0xff2a, + 0xff2a,0xff2a,0xff2a,0xff2a,0xff2a,0xff2b,0xff2b,0xff2b,0xff2b,0xff2b, + 0xff2b,0xff2b,0xff2b,0xff2b,0xff2b,0xff2b,0xff2c,0xff2c,0xff2c,0xff2c, + 0xff2c,0xff2c,0xff2c,0xff2c,0xff2c,0xff2c,0xff2c,0xff2d,0xff2d,0xff2d, + 0xff2d,0xff2d,0xff2d,0xff2d,0xff2d,0xff2d,0xff2d,0xff2e,0xff2e,0xff2e, + 0xff2e,0xff2e,0xff2e,0xff2e,0xff2e,0xff2e,0xff2e,0xff2e,0xff2f,0xff2f, + 0xff2f,0xff2f,0xff2f,0xff2f,0xff2f,0xff2f,0xff2f,0xff2f,0xff2f,0xff30, + 0xff30,0xff30,0xff30,0xff30,0xff30,0xff30,0xff30,0xff30,0xff30,0xff30, + 0xff31,0xff31,0xff31,0xff31,0xff31,0xff31,0xff31,0xff31,0xff31,0xff31, + 0xff32,0xff32,0xff32,0xff32,0xff32,0xff32,0xff32,0xff32,0xff32,0xff32, + 0xff32,0xff33,0xff33,0xff33,0xff33,0xff33,0xff33,0xff33,0xff33,0xff33, + 0xff33,0xff33,0xff34,0xff34,0xff34,0xff34,0xff34,0xff34,0xff34,0xff34, + 0xff34,0xff34,0xff35,0xff35,0xff35,0xff35,0xff35,0xff35,0xff35,0xff35, + 0xff35,0xff35,0xff35,0xff36,0xff36,0xff36,0xff36,0xff36,0xff36,0xff36, + 0xff36,0xff36,0xff36,0xff36,0xff37,0xff37,0xff37,0xff37,0xff37,0xff37, + 0xff37,0xff37,0xff37,0xff37,0xff37,0xff38,0xff38,0xff38,0xff38,0xff38, + 0xff38,0xff38,0xff38,0xff38,0xff38,0xff39,0xff39,0xff39,0xff39,0xff39, + 0xff39,0xff39,0xff39,0xff39,0xff39,0xff39,0xff3a,0xff3a,0xff3a,0xff3a, + 0xff3a,0xff3a,0xff3a,0xff3a,0xff3a,0xff3a,0xff3a,0xff3b,0xff3b,0xff3b, + 0xff3b,0xff3b,0xff3b,0xff3b,0xff3b,0xff3b,0xff3b,0xff3c,0xff3c,0xff3c, + 0xff3c,0xff3c,0xff3c,0xff3c,0xff3c,0xff3c,0xff3c,0xff3c,0xff3d,0xff3d, + 0xff3d,0xff3d,0xff3d,0xff3d,0xff3d,0xff3d,0xff3d,0xff3d,0xff3d,0xff3e, + 0xff3e,0xff3e,0xff3e,0xff3e,0xff3e,0xff3e,0xff3e,0xff3e,0xff3e,0xff3e, + 0xff3f,0xff3f,0xff3f,0xff3f,0xff3f,0xff3f,0xff3f,0xff3f,0xff3f,0xff3f, + 0xff40,0xff40,0xff40,0xff40,0xff40,0xff40,0xff40,0xff40,0xff40,0xff40, + 0xff40,0xff41,0xff41,0xff41,0xff41,0xff41,0xff41,0xff41,0xff41,0xff41, + 0xff41,0xff41,0xff42,0xff42,0xff42,0xff42,0xff42,0xff42,0xff42,0xff42, + 0xff42,0xff42,0xff42,0xff43,0xff43,0xff43,0xff43,0xff43,0xff43,0xff43, + 0xff43,0xff43,0xff43,0xff44,0xff44,0xff44,0xff44,0xff44,0xff44,0xff44, + 0xff44,0xff44,0xff44,0xff44,0xff45,0xff45,0xff45,0xff45,0xff45,0xff45, + 0xff45,0xff45,0xff45,0xff45,0xff45,0xff46,0xff46,0xff46,0xff46,0xff46, + 0xff46,0xff46,0xff46,0xff46,0xff46,0xff46,0xff47,0xff47,0xff47,0xff47, + 0xff47,0xff47,0xff47,0xff47,0xff47,0xff47,0xff48,0xff48,0xff48,0xff48, + 0xff48,0xff48,0xff48,0xff48,0xff48,0xff48,0xff48,0xff49,0xff49,0xff49, + 0xff49,0xff49,0xff49,0xff49,0xff49,0xff49,0xff49,0xff49,0xff4a,0xff4a, + 0xff4a,0xff4a,0xff4a,0xff4a,0xff4a,0xff4a,0xff4a,0xff4a,0xff4a,0xff4b, + 0xff4b,0xff4b,0xff4b,0xff4b,0xff4b,0xff4b,0xff4b,0xff4b,0xff4b,0xff4c, + 0xff4c,0xff4c,0xff4c,0xff4c,0xff4c,0xff4c,0xff4c,0xff4c,0xff4c,0xff4c, + 0xff4d,0xff4d,0xff4d,0xff4d,0xff4d,0xff4d,0xff4d,0xff4d,0xff4d,0xff4d, + 0xff4d,0xff4e,0xff4e,0xff4e,0xff4e,0xff4e,0xff4e,0xff4e,0xff4e,0xff4e, + 0xff4e,0xff4e,0xff4f,0xff4f,0xff4f,0xff4f,0xff4f,0xff4f,0xff4f,0xff4f, + 0xff4f,0xff4f,0xff50,0xff50,0xff50,0xff50,0xff50,0xff50,0xff50,0xff50, + 0xff50,0xff50,0xff50,0xff51,0xff51,0xff51,0xff51,0xff51,0xff51,0xff51, + 0xff51,0xff51,0xff51,0xff51,0xff52,0xff52,0xff52,0xff52,0xff52,0xff52, + 0xff52,0xff52,0xff52,0xff52,0xff52,0xff53,0xff53,0xff53,0xff53,0xff53, + 0xff53,0xff53,0xff53,0xff53,0xff53,0xff54,0xff54,0xff54,0xff54,0xff54, + 0xff54,0xff54,0xff54,0xff54,0xff54,0xff54,0xff55,0xff55,0xff55,0xff55, + 0xff55,0xff55,0xff55,0xff55,0xff55,0xff55,0xff55,0xff56,0xff56,0xff56, + 0xff56,0xff56,0xff56,0xff56,0xff56,0xff56,0xff56,0xff56,0xff57,0xff57, + 0xff57,0xff57,0xff57,0xff57,0xff57,0xff57,0xff57,0xff57,0xff57,0xff58, + 0xff58,0xff58,0xff58,0xff58,0xff58,0xff58,0xff58,0xff58,0xff58,0xff59, + 0xff59,0xff59,0xff59,0xff59,0xff59,0xff59,0xff59,0xff59,0xff59,0xff59, + 0xff5a,0xff5a,0xff5a,0xff5a,0xff5a,0xff5a,0xff5a,0xff5a,0xff5a,0xff5a, + 0xff5a,0xff5b,0xff5b,0xff5b,0xff5b,0xff5b,0xff5b,0xff5b,0xff5b,0xff5b, + 0xff5b,0xff5b,0xff5c,0xff5c,0xff5c,0xff5c,0xff5c,0xff5c,0xff5c,0xff5c, + 0xff5c,0xff5c,0xff5d,0xff5d,0xff5d,0xff5d,0xff5d,0xff5d,0xff5d,0xff5d, + 0xff5d,0xff5d,0xff5d,0xff5e,0xff5e,0xff5e,0xff5e,0xff5e,0xff5e,0xff5e, + 0xff5e,0xff5e,0xff5e,0xff5e,0xff5f,0xff5f,0xff5f,0xff5f,0xff5f,0xff5f, + 0xff5f,0xff5f,0xff5f,0xff5f,0xff5f,0xff60,0xff60,0xff60,0xff60,0xff60, + 0xff60,0xff60,0xff60,0xff60,0xff60,0xff60,0xff61,0xff61,0xff61,0xff61, + 0xff61,0xff61,0xff61,0xff61,0xff61,0xff61,0xff62,0xff62,0xff62,0xff62, + 0xff62,0xff62,0xff62,0xff62,0xff62,0xff62,0xff62,0xff63,0xff63,0xff63, + 0xff63,0xff63,0xff63,0xff63,0xff63,0xff63,0xff63,0xff63,0xff64,0xff64, + 0xff64,0xff64,0xff64,0xff64,0xff64,0xff64,0xff64,0xff64,0xff64,0xff65, + 0xff65,0xff65,0xff65,0xff65,0xff65,0xff65,0xff65,0xff65,0xff65,0xff65, + 0xff66,0xff66,0xff66,0xff66,0xff66,0xff66,0xff66,0xff66,0xff66,0xff66, + 0xff67,0xff67,0xff67,0xff67,0xff67,0xff67,0xff67,0xff67,0xff67,0xff67, + 0xff67,0xff68,0xff68,0xff68,0xff68,0xff68,0xff68,0xff68,0xff68,0xff68, + 0xff68,0xff68,0xff69,0xff69,0xff69,0xff69,0xff69,0xff69,0xff69,0xff69, + 0xff69,0xff69,0xff69,0xff6a,0xff6a,0xff6a,0xff6a,0xff6a,0xff6a,0xff6a, + 0xff6a,0xff6a,0xff6a,0xff6a,0xff6b,0xff6b,0xff6b,0xff6b,0xff6b,0xff6b, + 0xff6b,0xff6b,0xff6b,0xff6b,0xff6b,0xff6c,0xff6c,0xff6c,0xff6c,0xff6c, + 0xff6c,0xff6c,0xff6c,0xff6c,0xff6c,0xff6d,0xff6d,0xff6d,0xff6d,0xff6d, + 0xff6d,0xff6d,0xff6d,0xff6d,0xff6d,0xff6d,0xff6e,0xff6e,0xff6e,0xff6e, + 0xff6e,0xff6e,0xff6e,0xff6e,0xff6e,0xff6e,0xff6e,0xff6f,0xff6f,0xff6f, + 0xff6f,0xff6f,0xff6f,0xff6f,0xff6f,0xff6f,0xff6f,0xff6f,0xff70,0xff70, + 0xff70,0xff70,0xff70,0xff70,0xff70,0xff70,0xff70,0xff70,0xff70,0xff71, + 0xff71,0xff71,0xff71,0xff71,0xff71,0xff71,0xff71,0xff71,0xff71,0xff72, + 0xff72,0xff72,0xff72,0xff72,0xff72,0xff72,0xff72,0xff72,0xff72,0xff72, + 0xff73,0xff73,0xff73,0xff73,0xff73,0xff73,0xff73,0xff73,0xff73,0xff73, + 0xff73,0xff74,0xff74,0xff74,0xff74,0xff74,0xff74,0xff74,0xff74,0xff74, + 0xff74,0xff74,0xff75,0xff75,0xff75,0xff75,0xff75,0xff75,0xff75,0xff75, + 0xff75,0xff75,0xff75,0xff76,0xff76,0xff76,0xff76,0xff76,0xff76,0xff76, + 0xff76,0xff76,0xff76,0xff76,0xff77,0xff77,0xff77,0xff77,0xff77,0xff77, + 0xff77,0xff77,0xff77,0xff77,0xff78,0xff78,0xff78,0xff78,0xff78,0xff78, + 0xff78,0xff78,0xff78,0xff78,0xff78,0xff79,0xff79,0xff79,0xff79,0xff79, + 0xff79,0xff79,0xff79,0xff79,0xff79,0xff79,0xff7a,0xff7a,0xff7a,0xff7a, + 0xff7a,0xff7a,0xff7a,0xff7a,0xff7a,0xff7a,0xff7a,0xff7b,0xff7b,0xff7b, + 0xff7b,0xff7b,0xff7b,0xff7b,0xff7b,0xff7b,0xff7b,0xff7b,0xff7c,0xff7c, + 0xff7c,0xff7c,0xff7c,0xff7c,0xff7c,0xff7c,0xff7c,0xff7c,0xff7c,0xff7d, + 0xff7d,0xff7d,0xff7d,0xff7d,0xff7d,0xff7d,0xff7d,0xff7d,0xff7d,0xff7e, + 0xff7e,0xff7e,0xff7e,0xff7e,0xff7e,0xff7e,0xff7e,0xff7e,0xff7e,0xff7e, + 0xff7f,0xff7f,0xff7f,0xff7f,0xff7f,0xff7f,0xff7f,0xff7f,0xff7f,0xff7f, + 0xff7f,0xff80,0xff80,0xff80,0xff80,0xff80,0xff80,0xff80,0xff80,0xff80, + 0xff80,0xff80,0xff81,0xff81,0xff81,0xff81,0xff81,0xff81,0xff81,0xff81, + 0xff81,0xff81,0xff81,0xff82,0xff82,0xff82,0xff82,0xff82,0xff82,0xff82, + 0xff82,0xff82,0xff82,0xff82,0xff83,0xff83,0xff83,0xff83,0xff83,0xff83, + 0xff83,0xff83,0xff83,0xff83,0xff83,0xff84,0xff84,0xff84,0xff84,0xff84, + 0xff84,0xff84,0xff84,0xff84,0xff84,0xff85,0xff85,0xff85,0xff85,0xff85, + 0xff85,0xff85,0xff85,0xff85,0xff85,0xff85,0xff86,0xff86,0xff86,0xff86, + 0xff86,0xff86,0xff86,0xff86,0xff86,0xff86,0xff86,0xff87,0xff87,0xff87, + 0xff87,0xff87,0xff87,0xff87,0xff87,0xff87,0xff87,0xff87,0xff88,0xff88, + 0xff88,0xff88,0xff88,0xff88,0xff88,0xff88,0xff88,0xff88,0xff88,0xff89, + 0xff89,0xff89,0xff89,0xff89,0xff89,0xff89,0xff89,0xff89,0xff89,0xff89, + 0xff8a,0xff8a,0xff8a,0xff8a,0xff8a,0xff8a,0xff8a,0xff8a,0xff8a,0xff8a, + 0xff8a,0xff8b,0xff8b,0xff8b,0xff8b,0xff8b,0xff8b,0xff8b,0xff8b,0xff8b, + 0xff8b,0xff8b,0xff8c,0xff8c,0xff8c,0xff8c,0xff8c,0xff8c,0xff8c,0xff8c, + 0xff8c,0xff8c,0xff8d,0xff8d,0xff8d,0xff8d,0xff8d,0xff8d,0xff8d,0xff8d, + 0xff8d,0xff8d,0xff8d,0xff8e,0xff8e,0xff8e,0xff8e,0xff8e,0xff8e,0xff8e, + 0xff8e,0xff8e,0xff8e,0xff8e,0xff8f,0xff8f,0xff8f,0xff8f,0xff8f,0xff8f, + 0xff8f,0xff8f,0xff8f,0xff8f,0xff8f,0xff90,0xff90,0xff90,0xff90,0xff90, + 0xff90,0xff90,0xff90,0xff90,0xff90,0xff90,0xff91,0xff91,0xff91,0xff91, + 0xff91,0xff91,0xff91,0xff91,0xff91,0xff91,0xff91,0xff92,0xff92,0xff92, + 0xff92,0xff92,0xff92,0xff92,0xff92,0xff92,0xff92,0xff92,0xff93,0xff93, + 0xff93,0xff93,0xff93,0xff93,0xff93,0xff93,0xff93,0xff93,0xff93,0xff94, + 0xff94,0xff94,0xff94,0xff94,0xff94,0xff94,0xff94,0xff94,0xff94,0xff94, + 0xff95,0xff95,0xff95,0xff95,0xff95,0xff95,0xff95,0xff95,0xff95,0xff95, + 0xff96,0xff96,0xff96,0xff96,0xff96,0xff96,0xff96,0xff96,0xff96,0xff96, + 0xff96,0xff97,0xff97,0xff97,0xff97,0xff97,0xff97,0xff97,0xff97,0xff97, + 0xff97,0xff97,0xff98,0xff98,0xff98,0xff98,0xff98,0xff98,0xff98,0xff98, + 0xff98,0xff98,0xff98,0xff99,0xff99,0xff99,0xff99,0xff99,0xff99,0xff99, + 0xff99,0xff99,0xff99,0xff99,0xff9a,0xff9a,0xff9a,0xff9a,0xff9a,0xff9a, + 0xff9a,0xff9a,0xff9a,0xff9a,0xff9a,0xff9b,0xff9b,0xff9b,0xff9b,0xff9b, + 0xff9b,0xff9b,0xff9b,0xff9b,0xff9b,0xff9b,0xff9c,0xff9c,0xff9c,0xff9c, + 0xff9c,0xff9c,0xff9c,0xff9c,0xff9c,0xff9c,0xff9c,0xff9d,0xff9d,0xff9d, + 0xff9d,0xff9d,0xff9d,0xff9d,0xff9d,0xff9d,0xff9d,0xff9d,0xff9e,0xff9e, + 0xff9e,0xff9e,0xff9e,0xff9e,0xff9e,0xff9e,0xff9e,0xff9e,0xff9e,0xff9f, + 0xff9f,0xff9f,0xff9f,0xff9f,0xff9f,0xff9f,0xff9f,0xff9f,0xff9f,0xffa0, + 0xffa0,0xffa0,0xffa0,0xffa0,0xffa0,0xffa0,0xffa0,0xffa0,0xffa0,0xffa0, + 0xffa1,0xffa1,0xffa1,0xffa1,0xffa1,0xffa1,0xffa1,0xffa1,0xffa1,0xffa1, + 0xffa1,0xffa2,0xffa2,0xffa2,0xffa2,0xffa2,0xffa2,0xffa2,0xffa2,0xffa2, + 0xffa2,0xffa2,0xffa3,0xffa3,0xffa3,0xffa3,0xffa3,0xffa3,0xffa3,0xffa3, + 0xffa3,0xffa3,0xffa3,0xffa4,0xffa4,0xffa4,0xffa4,0xffa4,0xffa4,0xffa4, + 0xffa4,0xffa4,0xffa4,0xffa4,0xffa5,0xffa5,0xffa5,0xffa5,0xffa5,0xffa5, + 0xffa5,0xffa5,0xffa5,0xffa5,0xffa5,0xffa6,0xffa6,0xffa6,0xffa6,0xffa6, + 0xffa6,0xffa6,0xffa6,0xffa6,0xffa6,0xffa6,0xffa7,0xffa7,0xffa7,0xffa7, + 0xffa7,0xffa7,0xffa7,0xffa7,0xffa7,0xffa7,0xffa7,0xffa8,0xffa8,0xffa8, + 0xffa8,0xffa8,0xffa8,0xffa8,0xffa8,0xffa8,0xffa8,0xffa8,0xffa9,0xffa9, + 0xffa9,0xffa9,0xffa9,0xffa9,0xffa9,0xffa9,0xffa9,0xffa9,0xffa9,0xffaa, + 0xffaa,0xffaa,0xffaa,0xffaa,0xffaa,0xffaa,0xffaa,0xffaa,0xffaa,0xffaa, + 0xffab,0xffab,0xffab,0xffab,0xffab,0xffab,0xffab,0xffab,0xffab,0xffab, + 0xffab,0xffac,0xffac,0xffac,0xffac,0xffac,0xffac,0xffac,0xffac,0xffac, + 0xffac,0xffad,0xffad,0xffad,0xffad,0xffad,0xffad,0xffad,0xffad,0xffad, + 0xffad,0xffad,0xffae,0xffae,0xffae,0xffae,0xffae,0xffae,0xffae,0xffae, + 0xffae,0xffae,0xffae,0xffaf,0xffaf,0xffaf,0xffaf,0xffaf,0xffaf,0xffaf, + 0xffaf,0xffaf,0xffaf,0xffaf,0xffb0,0xffb0,0xffb0,0xffb0,0xffb0,0xffb0, + 0xffb0,0xffb0,0xffb0,0xffb0,0xffb0,0xffb1,0xffb1,0xffb1,0xffb1,0xffb1, + 0xffb1,0xffb1,0xffb1,0xffb1,0xffb1,0xffb1,0xffb2,0xffb2,0xffb2,0xffb2, + 0xffb2,0xffb2,0xffb2,0xffb2,0xffb2,0xffb2,0xffb2,0xffb3,0xffb3,0xffb3, + 0xffb3,0xffb3,0xffb3,0xffb3,0xffb3,0xffb3,0xffb3,0xffb3,0xffb4,0xffb4, + 0xffb4,0xffb4,0xffb4,0xffb4,0xffb4,0xffb4,0xffb4,0xffb4,0xffb4,0xffb5, + 0xffb5,0xffb5,0xffb5,0xffb5,0xffb5,0xffb5,0xffb5,0xffb5,0xffb5,0xffb5, + 0xffb6,0xffb6,0xffb6,0xffb6,0xffb6,0xffb6,0xffb6,0xffb6,0xffb6,0xffb6, + 0xffb6,0xffb7,0xffb7,0xffb7,0xffb7,0xffb7,0xffb7,0xffb7,0xffb7,0xffb7, + 0xffb7,0xffb7,0xffb8,0xffb8,0xffb8,0xffb8,0xffb8,0xffb8,0xffb8,0xffb8, + 0xffb8,0xffb8,0xffb8,0xffb9,0xffb9,0xffb9,0xffb9,0xffb9,0xffb9,0xffb9, + 0xffb9,0xffb9,0xffb9,0xffb9,0xffba,0xffba,0xffba,0xffba,0xffba,0xffba, + 0xffba,0xffba,0xffba,0xffba,0xffba,0xffbb,0xffbb,0xffbb,0xffbb,0xffbb, + 0xffbb,0xffbb,0xffbb,0xffbb,0xffbb,0xffbb,0xffbc,0xffbc,0xffbc,0xffbc, + 0xffbc,0xffbc,0xffbc,0xffbc,0xffbc,0xffbc,0xffbc,0xffbd,0xffbd,0xffbd, + 0xffbd,0xffbd,0xffbd,0xffbd,0xffbd,0xffbd,0xffbd,0xffbd,0xffbe,0xffbe, + 0xffbe,0xffbe,0xffbe,0xffbe,0xffbe,0xffbe,0xffbe,0xffbe,0xffbe,0xffbf, + 0xffbf,0xffbf,0xffbf,0xffbf,0xffbf,0xffbf,0xffbf,0xffbf,0xffbf,0xffbf, + 0xffc0,0xffc0,0xffc0,0xffc0,0xffc0,0xffc0,0xffc0,0xffc0,0xffc0,0xffc0, + 0xffc0,0xffc1,0xffc1,0xffc1,0xffc1,0xffc1,0xffc1,0xffc1,0xffc1,0xffc1, + 0xffc1,0xffc2,0xffc2,0xffc2,0xffc2,0xffc2,0xffc2,0xffc2,0xffc2,0xffc2, + 0xffc2,0xffc2,0xffc3,0xffc3,0xffc3,0xffc3,0xffc3,0xffc3,0xffc3,0xffc3, + 0xffc3,0xffc3,0xffc3,0xffc4,0xffc4,0xffc4,0xffc4,0xffc4,0xffc4,0xffc4, + 0xffc4,0xffc4,0xffc4,0xffc4,0xffc5,0xffc5,0xffc5,0xffc5,0xffc5,0xffc5, + 0xffc5,0xffc5,0xffc5,0xffc5,0xffc5,0xffc6,0xffc6,0xffc6,0xffc6,0xffc6, + 0xffc6,0xffc6,0xffc6,0xffc6,0xffc6,0xffc6,0xffc7,0xffc7,0xffc7,0xffc7, + 0xffc7,0xffc7,0xffc7,0xffc7,0xffc7,0xffc7,0xffc7,0xffc8,0xffc8,0xffc8, + 0xffc8,0xffc8,0xffc8,0xffc8,0xffc8,0xffc8,0xffc8,0xffc8,0xffc9,0xffc9, + 0xffc9,0xffc9,0xffc9,0xffc9,0xffc9,0xffc9,0xffc9,0xffc9,0xffc9,0xffca, + 0xffca,0xffca,0xffca,0xffca,0xffca,0xffca,0xffca,0xffca,0xffca,0xffca, + 0xffcb,0xffcb,0xffcb,0xffcb,0xffcb,0xffcb,0xffcb,0xffcb,0xffcb,0xffcb, + 0xffcb,0xffcc,0xffcc,0xffcc,0xffcc,0xffcc,0xffcc,0xffcc,0xffcc,0xffcc, + 0xffcc,0xffcc,0xffcd,0xffcd,0xffcd,0xffcd,0xffcd,0xffcd,0xffcd,0xffcd, + 0xffcd,0xffcd,0xffcd,0xffce,0xffce,0xffce,0xffce,0xffce,0xffce,0xffce, + 0xffce,0xffce,0xffce,0xffce,0xffcf,0xffcf,0xffcf,0xffcf,0xffcf,0xffcf, + 0xffcf,0xffcf,0xffcf,0xffcf,0xffcf,0xffd0,0xffd0,0xffd0,0xffd0,0xffd0, + 0xffd0,0xffd0,0xffd0,0xffd0,0xffd0,0xffd0,0xffd1,0xffd1,0xffd1,0xffd1, + 0xffd1,0xffd1,0xffd1,0xffd1,0xffd1,0xffd1,0xffd1,0xffd2,0xffd2,0xffd2, + 0xffd2,0xffd2,0xffd2,0xffd2,0xffd2,0xffd2,0xffd2,0xffd2,0xffd3,0xffd3, + 0xffd3,0xffd3,0xffd3,0xffd3,0xffd3,0xffd3,0xffd3,0xffd3,0xffd3,0xffd4, + 0xffd4,0xffd4,0xffd4,0xffd4,0xffd4,0xffd4,0xffd4,0xffd4,0xffd4,0xffd4, + 0xffd5,0xffd5,0xffd5,0xffd5,0xffd5,0xffd5,0xffd5,0xffd5,0xffd5,0xffd5, + 0xffd5,0xffd6,0xffd6,0xffd6,0xffd6,0xffd6,0xffd6,0xffd6,0xffd6,0xffd6, + 0xffd6,0xffd6,0xffd7,0xffd7,0xffd7,0xffd7,0xffd7,0xffd7,0xffd7,0xffd7, + 0xffd7,0xffd7,0xffd7,0xffd8,0xffd8,0xffd8,0xffd8,0xffd8,0xffd8,0xffd8, + 0xffd8,0xffd8,0xffd8,0xffd8,0xffd9,0xffd9,0xffd9,0xffd9,0xffd9,0xffd9, + 0xffd9,0xffd9,0xffd9,0xffd9,0xffd9,0xffda,0xffda,0xffda,0xffda,0xffda, + 0xffda,0xffda,0xffda,0xffda,0xffda,0xffda,0xffdb,0xffdb,0xffdb,0xffdb, + 0xffdb,0xffdb,0xffdb,0xffdb,0xffdb,0xffdb,0xffdb,0xffdc,0xffdc,0xffdc, + 0xffdc,0xffdc,0xffdc,0xffdc,0xffdc,0xffdc,0xffdc,0xffdc,0xffdd,0xffdd, + 0xffdd,0xffdd,0xffdd,0xffdd,0xffdd,0xffdd,0xffdd,0xffdd,0xffdd,0xffdd, + 0xffde,0xffde,0xffde,0xffde,0xffde,0xffde,0xffde,0xffde,0xffde,0xffde, + 0xffde,0xffdf,0xffdf,0xffdf,0xffdf,0xffdf,0xffdf,0xffdf,0xffdf,0xffdf, + 0xffdf,0xffdf,0xffe0,0xffe0,0xffe0,0xffe0,0xffe0,0xffe0,0xffe0,0xffe0, + 0xffe0,0xffe0,0xffe0,0xffe1,0xffe1,0xffe1,0xffe1,0xffe1,0xffe1,0xffe1, + 0xffe1,0xffe1,0xffe1,0xffe1,0xffe2,0xffe2,0xffe2,0xffe2,0xffe2,0xffe2, + 0xffe2,0xffe2,0xffe2,0xffe2,0xffe2,0xffe3,0xffe3,0xffe3,0xffe3,0xffe3, + 0xffe3,0xffe3,0xffe3,0xffe3,0xffe3,0xffe3,0xffe4,0xffe4,0xffe4,0xffe4, + 0xffe4,0xffe4,0xffe4,0xffe4,0xffe4,0xffe4,0xffe4,0xffe5,0xffe5,0xffe5, + 0xffe5,0xffe5,0xffe5,0xffe5,0xffe5,0xffe5,0xffe5,0xffe5,0xffe6,0xffe6, + 0xffe6,0xffe6,0xffe6,0xffe6,0xffe6,0xffe6,0xffe6,0xffe6,0xffe6,0xffe7, + 0xffe7,0xffe7,0xffe7,0xffe7,0xffe7,0xffe7,0xffe7,0xffe7,0xffe7,0xffe7, + 0xffe8,0xffe8,0xffe8,0xffe8,0xffe8,0xffe8,0xffe8,0xffe8,0xffe8,0xffe8, + 0xffe8,0xffe9,0xffe9,0xffe9,0xffe9,0xffe9,0xffe9,0xffe9,0xffe9,0xffe9, + 0xffe9,0xffe9,0xffea,0xffea,0xffea,0xffea,0xffea,0xffea,0xffea,0xffea, + 0xffea,0xffea,0xffea,0xffeb,0xffeb,0xffeb,0xffeb,0xffeb,0xffeb,0xffeb, + 0xffeb,0xffeb,0xffeb,0xffeb,0xffec,0xffec,0xffec,0xffec,0xffec,0xffec, + 0xffec,0xffec,0xffec,0xffec,0xffec,0xffed,0xffed,0xffed,0xffed,0xffed, + 0xffed,0xffed,0xffed,0xffed,0xffed,0xffed,0xffee,0xffee,0xffee,0xffee, + 0xffee,0xffee,0xffee,0xffee,0xffee,0xffee,0xffee,0xffef,0xffef,0xffef, + 0xffef,0xffef,0xffef,0xffef,0xffef,0xffef,0xffef,0xffef,0xfff0,0xfff0, + 0xfff0,0xfff0,0xfff0,0xfff0,0xfff0,0xfff0,0xfff0,0xfff0,0xfff0,0xfff1, + 0xfff1,0xfff1,0xfff1,0xfff1,0xfff1,0xfff1,0xfff1,0xfff1,0xfff1,0xfff1, + 0xfff2,0xfff2,0xfff2,0xfff2,0xfff2,0xfff2,0xfff2,0xfff2,0xfff2,0xfff2, + 0xfff2,0xfff3,0xfff3,0xfff3,0xfff3,0xfff3,0xfff3,0xfff3,0xfff3,0xfff3, + 0xfff3,0xfff3,0xfff3,0xfff4,0xfff4,0xfff4,0xfff4,0xfff4,0xfff4,0xfff4, + 0xfff4,0xfff4,0xfff4,0xfff4,0xfff5,0xfff5,0xfff5,0xfff5,0xfff5,0xfff5, + 0xfff5,0xfff5,0xfff5,0xfff5,0xfff5,0xfff6,0xfff6,0xfff6,0xfff6,0xfff6, + 0xfff6,0xfff6,0xfff6,0xfff6,0xfff6,0xfff6,0xfff7,0xfff7,0xfff7,0xfff7, + 0xfff7,0xfff7,0xfff7,0xfff7,0xfff7,0xfff7,0xfff7,0xfff8,0xfff8,0xfff8, + 0xfff8,0xfff8,0xfff8,0xfff8,0xfff8,0xfff8,0xfff8,0xfff8,0xfff9,0xfff9, + 0xfff9,0xfff9,0xfff9,0xfff9,0xfff9,0xfff9,0xfff9,0xfff9,0xfff9,0xfffa, + 0xfffa,0xfffa,0xfffa,0xfffa,0xfffa,0xfffa,0xfffa,0xfffa,0xfffa,0xfffa, + 0xfffb,0xfffb,0xfffb,0xfffb,0xfffb,0xfffb,0xfffb,0xfffb,0xfffb,0xfffb, + 0xfffb,0xfffc,0xfffc,0xfffc,0xfffc,0xfffc,0xfffc,0xfffc,0xfffc,0xfffc, + 0xfffc,0xfffc,0xfffd,0xfffd,0xfffd,0xfffd,0xfffd,0xfffd,0xfffd,0xfffd, + 0xfffd,0xfffd,0xfffd,0xfffe,0xfffe,0xfffe,0xfffe,0xfffe,0xfffe,0xfffe, + 0xfffe,0xfffe,0xfffe,0xfffe,0xffff,0xffff,0xffff,0xffff,0xffff,0xffff, + 0xffff,0xffff,0xffff,0xffff,0xffff,0xffff +}; diff --git a/src/crush/generate_ln_table.c b/src/crush/generate_ln_table.c new file mode 100644 index 000000000000..356374d9a103 --- /dev/null +++ b/src/crush/generate_ln_table.c @@ -0,0 +1,36 @@ +#include +#include + +unsigned fake_ln(unsigned x) +{ + double ln = log((double)(x+1) / (double)0x10000); + ln += 11.090355; + unsigned y = ln * (double)0x10000 / 11.090355; + if (y > 0xffff) + y = 0xffff; + return y; +} + +int main(int argc, char **argv) +{ + int i; + double min = -11.090355; + double max = 0; + int target_max = 0x10000; + printf("static uint16_t crush_ln_table[65536] = {"); + for (i = 0; i < 0x10000; ++i) { + double ln = log((double)(i+1) / (double)0x10000); + double ln2 = (ln - min); + unsigned x = (ln2) * (target_max / (max - min)); + //printf("%x\t%lf\t%lf\t%x\t%x\n", i, ln, ln2, x, fake_ln(i)); + if (i % 10 == 0) { + if (i) + printf(","); + printf("\n\t"); + } else { + printf(","); + } + printf("0x%x", fake_ln(i)); + } + printf("\n};\n"); +} diff --git a/src/crush/grammar.h b/src/crush/grammar.h index 42b0b8ef777f..61709185ef58 100644 --- a/src/crush/grammar.h +++ b/src/crush/grammar.h @@ -116,7 +116,8 @@ struct crush_grammar : public grammar bucket_alg = str_p("alg") >> ( str_p("uniform") | str_p("list") | str_p("tree") | - str_p("straw") ); + str_p("straw") | + str_p("straw2")); bucket_hash = str_p("hash") >> ( integer | str_p("rjenkins1") ); bucket_item = str_p("item") >> name diff --git a/src/crush/mapper.c b/src/crush/mapper.c index 2de70eb573ed..7532765cadc3 100644 --- a/src/crush/mapper.c +++ b/src/crush/mapper.c @@ -22,6 +22,7 @@ #include "crush.h" #include "hash.h" +#include "crush_ln_table.h" /* * Implement the core CRUSH mapping algorithm. @@ -239,6 +240,52 @@ static int bucket_straw_choose(struct crush_bucket_straw *bucket, return bucket->h.items[high]; } +/* + * straw2 + * + * for reference, see: + * + * http://en.wikipedia.org/wiki/Exponential_distribution#Distribution_of_the_minimum_of_exponential_random_variables + * + */ + +static int bucket_straw2_choose(struct crush_bucket_straw2 *bucket, + int x, int r) +{ + unsigned i, high = 0; + unsigned u; + __s64 ln, draw, high_draw = 0; + + for (i = 0; i < bucket->h.size; i++) { + u = crush_hash32_3(bucket->h.hash, x, bucket->h.items[i], r); + u &= 0xffff; + + /* + * for some reason slightly less than 0x10000 produces + * a slightly more accurate distribution... probably a + * rounding effect. + * + * the natural log lookup table maps [0,0xffff] + * (corresponding to real numbers [1/0x10000, 1] to + * [0, 0xffff] (corresponding to real numbers + * [-11.090355,0]). + */ + ln = crush_ln_table[u] - 0xfffc; + + /* + * divide by 16.16 fixed-point weight + */ + draw = (ln << 32) / bucket->item_weights[i]; + + if (i == 0 || draw > high_draw) { + high = i; + high_draw = draw; + } + } + return bucket->h.items[high]; +} + + static int crush_bucket_choose(struct crush_bucket *in, int x, int r) { dprintk(" crush_bucket_choose %d x=%d r=%d\n", in->id, x, r); @@ -256,12 +303,16 @@ static int crush_bucket_choose(struct crush_bucket *in, int x, int r) case CRUSH_BUCKET_STRAW: return bucket_straw_choose((struct crush_bucket_straw *)in, x, r); + case CRUSH_BUCKET_STRAW2: + return bucket_straw2_choose((struct crush_bucket_straw2 *)in, + x, r); default: dprintk("unknown bucket %d alg %d\n", in->id, in->alg); return in->items[0]; } } + /* * true if device is marked "out" (failed, fully offloaded) * of the cluster diff --git a/src/test/crush/crush.cc b/src/test/crush/crush.cc index cb0226d164be..83d5a2f1e636 100644 --- a/src/test/crush/crush.cc +++ b/src/test/crush/crush.cc @@ -411,6 +411,232 @@ TEST(CRUSH, straw_same) { ASSERT_LT(ratio, .001); } +double calc_straw2_stddev(int *weights, int n, bool verbose) +{ + CrushWrapper *c = new CrushWrapper; + const int ROOT_TYPE = 2; + c->set_type_name(ROOT_TYPE, "root"); + const int HOST_TYPE = 1; + c->set_type_name(HOST_TYPE, "host"); + const int OSD_TYPE = 0; + c->set_type_name(OSD_TYPE, "osd"); + + int items[n]; + for (int i=0; i set_max_devices(n); + + string root_name0("root0"); + int root0; + crush_bucket *b0 = crush_make_bucket(c->get_crush_map(), + CRUSH_BUCKET_STRAW2, CRUSH_HASH_RJENKINS1, + ROOT_TYPE, n, items, weights); + crush_add_bucket(c->get_crush_map(), 0, b0, &root0); + c->set_item_name(root0, root_name0); + + string name0("rule0"); + int ruleset0 = c->add_simple_ruleset(name0, root_name0, "osd", + "firstn", pg_pool_t::TYPE_REPLICATED); + + int sum[n]; + double totalweight = 0; + vector reweight(n); + for (int i=0; i out; + c->do_rule(ruleset0, i, out, 1, reweight); + sum[out[0]]++; + } + + double expected = (double)total / (double)n; + if (verbose) + cout << "expect\t\t\t" << expected << std::endl; + double stddev = 0; + double exptotal = 0; + if (verbose) + cout << "osd\tweight\tcount\tadjusted\n"; + std::streamsize p = cout.precision(); + cout << std::setprecision(4); + for (int i=0; iset_type_name(ROOT_TYPE, "root"); + const int HOST_TYPE = 1; + c->set_type_name(HOST_TYPE, "host"); + const int OSD_TYPE = 0; + c->set_type_name(OSD_TYPE, "osd"); + + int items[n]; + for (int i=0; i set_max_devices(n); + + string root_name0("root0"); + int root0; + crush_bucket *b0 = crush_make_bucket(c->get_crush_map(), + CRUSH_BUCKET_STRAW2, CRUSH_HASH_RJENKINS1, + ROOT_TYPE, n, items, weights); + EXPECT_EQ(0, crush_add_bucket(c->get_crush_map(), 0, b0, &root0)); + EXPECT_EQ(0, c->set_item_name(root0, root_name0)); + + string name0("rule0"); + int ruleset0 = c->add_simple_ruleset(name0, root_name0, "osd", + "firstn", pg_pool_t::TYPE_REPLICATED); + EXPECT_EQ(0, ruleset0); + + int changed = 1; + weights[changed] = weights[changed] / 10 * (rand() % 10); + + string root_name1("root1"); + int root1; + crush_bucket *b1 = crush_make_bucket(c->get_crush_map(), + CRUSH_BUCKET_STRAW2, CRUSH_HASH_RJENKINS1, + ROOT_TYPE, n, items, weights); + EXPECT_EQ(0, crush_add_bucket(c->get_crush_map(), 0, b1, &root1)); + EXPECT_EQ(0, c->set_item_name(root1, root_name1)); + + string name1("rule1"); + int ruleset1 = c->add_simple_ruleset(name1, root_name1, "osd", + "firstn", pg_pool_t::TYPE_REPLICATED); + EXPECT_EQ(1, ruleset1); + + int sum[n]; + double totalweight = 0; + vector reweight(n); + for (int i=0; i out0, out1; + c->do_rule(ruleset0, i, out0, 1, reweight); + ASSERT_EQ(1, out0.size()); + + c->do_rule(ruleset1, i, out1, 1, reweight); + ASSERT_EQ(1, out1.size()); + + sum[out1[0]]++; + //sum[rand()%n]++; + + if (out1[0] == changed) + ASSERT_EQ(changed, out0[0]); + else if (out0[0] != changed) + ASSERT_EQ(out0[0], out1[0]); + } + + double expected = (double)total / (double)n; + cout << "expect\t\t\t" << expected << std::endl; + double stddev = 0; + cout << "osd\tweight\tcount\tadjusted\n"; + std::streamsize p = cout.precision(); + cout << std::setprecision(4); + for (int i=0; i args; diff --git a/src/tools/crushtool.cc b/src/tools/crushtool.cc index 80438d85276f..cb3d628ca4dc 100644 --- a/src/tools/crushtool.cc +++ b/src/tools/crushtool.cc @@ -151,6 +151,7 @@ struct bucket_types_t { { "uniform", CRUSH_BUCKET_UNIFORM }, { "list", CRUSH_BUCKET_LIST }, { "straw", CRUSH_BUCKET_STRAW }, + { "straw2", CRUSH_BUCKET_STRAW2 }, { "tree", CRUSH_BUCKET_TREE }, { 0, 0 }, };